Polytope of Type {28,4,2} with group SmallGroup(448,940)

Overview

Group: SmallGroup(448,940)
Rank: 4
Schläfli Type: {28,4,2}
Vertices, edges, …: 28, 56, 4, 2
Order of s₀s₁s₂s₃: 28
Order of s₀s₁s₂s₃s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Degenerate
Universal
Orientable
Flat

Related Polytopes

Constructions

Facet of

Vertex figure of

Quotients maximal quotients in bold

2-fold

4-fold

{14,2,2}*112

7-fold

{4,4,2}*64

8-fold

{7,2,2}*56

14-fold

28-fold

{2,2,2}*16

Covers minimal covers in bold

2-fold

3-fold

4-fold

Representations

Permutation Representation (GAP)

s0 := ( 2, 7)( 3, 6)( 4, 5)( 9,14)(10,13)(11,12)(16,21)(17,20)(18,19)(23,28)(24,27)(25,26)(29,43)(30,49)(31,48)(32,47)(33,46)(34,45)(35,44)(36,50)(37,56)(38,55)(39,54)(40,53)(41,52)(42,51);;
s1 := ( 1,30)( 2,29)( 3,35)( 4,34)( 5,33)( 6,32)( 7,31)( 8,37)( 9,36)(10,42)(11,41)(12,40)(13,39)(14,38)(15,44)(16,43)(17,49)(18,48)(19,47)(20,46)(21,45)(22,51)(23,50)(24,56)(25,55)(26,54)(27,53)(28,52);;
s2 := (29,36)(30,37)(31,38)(32,39)(33,40)(34,41)(35,42)(43,50)(44,51)(45,52)(46,53)(47,54)(48,55)(49,56);;
s3 := (57,58);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP)

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(58)!( 2, 7)( 3, 6)( 4, 5)( 9,14)(10,13)(11,12)(16,21)(17,20)(18,19)(23,28)(24,27)(25,26)(29,43)(30,49)(31,48)(32,47)(33,46)(34,45)(35,44)(36,50)(37,56)(38,55)(39,54)(40,53)(41,52)(42,51);
s1 := Sym(58)!( 1,30)( 2,29)( 3,35)( 4,34)( 5,33)( 6,32)( 7,31)( 8,37)( 9,36)(10,42)(11,41)(12,40)(13,39)(14,38)(15,44)(16,43)(17,49)(18,48)(19,47)(20,46)(21,45)(22,51)(23,50)(24,56)(25,55)(26,54)(27,53)(28,52);
s2 := Sym(58)!(29,36)(30,37)(31,38)(32,39)(33,40)(34,41)(35,42)(43,50)(44,51)(45,52)(46,53)(47,54)(48,55)(49,56);
s3 := Sym(58)!(57,58);
poly := sub<Sym(58)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma)

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;